The existing handbrake cable is not the original but I assume it is the same type. It is a wire rope comprising 7 bundles of 19 strands of 11.5thou diameter steel wire. The overall diameter is about 0.15" (3.7mm). Bought some 4mm stainless steel 7x19 wire rope but that seems much too thick for the pulleys so got some 3mm rope, which should be satisfactory.
The pulleys are in very poor condition and will have to be replaced. The current ones have a semicircular groove with a radius of radius 0.125" (3.2mm) and would not be too difficult to fabricate.